Analysis of the Behavior of Low-Noise Asphalt Mixtures with Modified Binders under Sinusoidal Loading

The paper presents the results of tests of the stiffness modulus according to the 4PB-PR method of low-noise asphalt mixtures with the addition of rubber granulate (RG). Mixtures of this type are characterized by an increased air void content (about 10–25%). This causes a rapid bitumen oxidation, which results in oxidative hardening, contributing to a faster deterioration of the properties of the mixtures. This means that binders of appropriate quality should be used in the process of producing asphalt mixtures, which will provide the mixtures with sufficiently high technical properties. The tested asphalt mixtures are differentiated according to the type of bitumen modifiers: styrene–butadiene–styrene copolymer (SBS) and crumb rubber (CR). The article presents the tests results of the stiffness modulus using the 4PB-PR method. This test has a high correlation with regard to “in situ” tests. The research proved that each of the modifiers used increased the stiffness modulus of low-noise asphalt mixtures. Replacing the mineral aggregate with 30% RG leads to a tenfold decrease in the stiffness modulus. In the entire range of analyzed temperatures, mixtures with the use of modifiers show higher values of the elastic component of the stiffness modulus, as evidenced by lower values of the phase angle.


Introduction
The 20th century was characterized by the rapid development of road traffic [1]. During this period, road pavements built in Poland, due to the type of structure and the materials used, did not fully reduce the noise that was increasing all the time. This phenomenon attracted the attention of many researchers and contributed to the creation of low-noise asphalt pavements. Such pavements include, among others: BBTM (French for Beton Bitumineux Tres Mince), SDA (Semi-Dense Asphalt), PA (Porous Asphalt), noise reduced stone mastic asphalt SMA LA (German for Lärm Arm), PERS (Poroelastic Road Surface) [2]. Research has shown that the use of such mixtures for the wearing course of road pavements allows the reduction of noise to 10-12 dB [3,4]. Asphalt mixtures from this group are characterized by air void content in the range of 15-25%. Many studies [5,6] have shown that higher air void content contributes to the formation of carbonyl groups in the binder, resulting in oxidative hardening, which causes faster pavement degradation. Therefore, to produce "quiet" mixtures, it is required to properly select bitumen binders with high technical parameters, particularly with the increased resistance to long-term (in-service) aging [7].
The quality of the raw material used in the distillation process of the crude oil has a huge impact on the properties of road bitumen, which was used in the production of asphalt mixture. Unfortunately, in recent years there has been a trend to refine light crude oil (increasing fuel profit), which has reduced the distillation residue from 20% to 10% or less. For this reason, the quality of industrially produced bitumen does not meet the requirements for use in "quiet" pavements, which has been confirmed by investigations However, the influence of rubber granulate (RG) on changes in stiffness modulus by the 4PB-PR method of "quiet" mixtures has not yet been investigated, which is an important aspect in the design of this type of pavement.
The aim of the research presented in this paper is to analyze the effect of the type of modification of bitumen binders with SBS polymer and CR and the addition of RG (1/4 mm fraction) on the change of technical parameters (stiffness modulus and phase angle) in the four-point bending study with prismatic samples 4PB-PR of low-noise asphalt mixtures.
Chapter 2 presents the characteristics and properties of the materials used for the designed asphalt mixtures (PA8, SMA8 and SMA8 LA) and mineral-rubber-asphalt mixtures SMA8 LA (10% RG), SMA8 LA (20% RG), SMA8 LA (30% RG). The grain size distribution (percentage of material passing through the sieve), binder content, air void content, and density of mixtures are given. The basics and principles of determining the stiffness modulus and phase angle according to the four-point bending with prismatic samples (4PB-PR) are also discussed.
Chapter 3 presents and discusses the results of tests of stiffness modulus 4PB-PR for conventional asphalt mixtures and results of tests of stiffness modulus for asphalt mixtures with the addition of RG, change of the phase angle Φ at variable temperature and frequency for conventional asphalt mixtures and change of the phase angle Φ at variable temperature and frequency for asphalt mixtures with the addition of RG. A discussion of the results in comparison with the findings of other researchers presented in the literature is also provided.
The technical properties of the modified binders before and after the RTFOT (rolling thin film oven test) technological aging process are presented in Table 1. Detailed test results of bitumen binders and aggregates used for asphalt mixtures are described in publications [37,38].

Used Additives for Binders and Asphalt Mixtures
Modified binders were obtained in the "wet process". Kraton D1192 which is a linear triblock polymer with 30% styrene content by mass, was used for the preparation of polymer bitumen. Information on the basic chemical properties of the SBS copolymer is presented in Table 2. The rubber-asphalt binder was prepared on the basis of CR with a grain size of 0/0.8 mm. The grain size analysis of the CR is presented in Table 3. In the mixtures with increased flexibility, part of the aggregate in the "dry process" was replaced with RG with a grain size of 1/4 mm. The sieve analysis of the granulate is presented in Table 4. Bitumen with a penetration of 50/70 was used for the production of modified binders. Bitumen was heated to a temperature of 180 • C. A measured amount of modifier (5% SBS copolymer or 10% CR, or 2% SBS copolymer and 10% CR) was gradually added to the bitumen and mixed for 1 h at a constant speed of 700 rpm [39]. Then, using the RTFOT device, the binder was subjected to the test simulating the process of technological aging according to [40].
Before being added to the mix, RG was preheated, which caused a swelling effect and a "slight" devulcanization of the rubber to allow the binder to bond with the rubber more effectively. In mineral-rubber-asphalt mixtures, part of the mineral aggregate was replaced with RG in the amount of 10%, 20%, and 30% in relation to the mixture volume in order to improve their flexibility.

Designed Low-Noise Asphalt Mixtures
The following asphalt mixtures and low-noise mineral-rubber-asphalt mixtures were used for laboratory tests: porous asphalt (PA8), stone mastic asphalt (SMA8), stone mastic asphalt reducing tire/road noise (SMA8 LA), and stone mastic asphalt reducing tire/road noise with 10% (SMA8 LA [10% RG]), 20% (SMA8 LA [20% RG]), and 30% (SMA8 LA [30% RG]). The mixtures were prepared in a laboratory mixer which set up a 3-dimensional counter-rotating mixing process with an eccentric rotary agitator. Before compacting, the mixtures were spread into a thin layer and for 2 h subjected to thermostating in a dryer at the temperature of 145 ± 5 • C with the reference binder and at 155 ± 5 • C for the modified binder. Such a procedure made it possible to bring the mixture preparation process closer to the conditions in an asphalt plant and is required by the standard [41]. The samples for 4PB-PR tests were prepared according to [42] in a slab roller compactor with the dimensions of the plates 300 mm × 400 mm × 80 mm. Then, rectangular beams with dimensions of 50 mm × 63 mm × 400 mm were cut from these plates.
The binder content, air void content, grain size composition, and density of the designed asphalt mixtures are presented in Table 5 and Figure 1.
The particle size distribution of tested mixtures [39].
Particle size distribution of tested mixtures ( Figure 1) indicate that the tested mixtures are characterized by discontinuous grain size. The presented curves show that the PA8 mixture contains the most air voids, and the SMA8 mixture has the least air voids. When comparing SMA8 LA mixtures, it was concluded that increasing the addition of rubber granulate approximates the grain size curves of SMA8 LA mixtures with granulate to the SMA8 mixture. This is an advantageous solution due to the noisiness of the pavement as the air void content in such mixtures increases compared to SMA8 LA. The stiffness of asphalt mixtures has a significant impact on the stress level generated in the structural layers of the road surface by traffic loads and temperature changes during operation. These stresses determine the resistance to fatigue and cracking of the pavement. The stiffness modules by the four-point bending method were tested according to [43]. The loads applied to the sample were cyclic and sinusoidal, which is typical in real conditions. The thermostatic time at the test temperature was 1 h. According to [43], the samples were rotated 90 • along the longitudinal compaction axis in the slab. The stiffness modulus was determined at the 100th load cycle. Due to the fact that asphalt mixture is a typical visco-elastic material, its mechanical properties largely depend on the test temperature and frequency. Therefore, it was decided to perform tests in a wide temperature range: 5 • C, 15 • C, 25 • C and at the following frequencies: 0.5 Hz, 1.0 Hz, 5.0 Hz, 10 Hz, 20 Hz.
The value of the stiffness modulus is defined as the absolute value of the complex modulus, |E *|, determined from the dependency between the stress and the deformation at time t. Characteristic for viscoelastic materials is the shift of the stress curve in relation to the deformation curve by the value of the phase angle, Φ ( Figure 2). Perfectly elastic bodies are characterized by a phase angle, Φ = 0 • . In viscous bodies, the phase angle fluctuates around 90 • . For visco-elastic bodies, the angle value ranges from 0 • to 90 • .
The stiffness modulus consists of the real (E 1 ) and the imaginary (E 2 ) component: The real component is determined according to the Equation (2): where: ; ω-angular frequency (rad/s). The imaginary component is calculated according to the Dependency (3): The mass and shape coefficients are calculated according to the Formulas (4)- (7): where: L-distance between outer supports (m); B-sample width (m); H-sample height (m); M-sample mass (kg); m-mass of the moving parts of the device (kg); l-distance between places of sample loading (m); A-distance between the outer clamp and the next inner clamp (m); x-position of the probe for measuring beam deformation (m).
Phase angle is defined as the phase difference between stress and strain and is determined by Equation (8): where: B ε -phase angle of the approximate function of the strain value (rad); B t -phase angle of the approximate function of the stress value (rad).

Stiffness Modulus 4PB-PR
The results of testing the stiffness modulus with the 4PB-PR method at different frequencies at temperatures 5 • C, 15 • C, and 25 • C are shown in Tables 6 and 7, while the change of the stiffness modulus values as a function of temperature at 10 Hz is shown in Figure 3.  The results of the 4PB-PR stiffness modulus tests presented in this study confirm the previous research results described in publications [44][45][46][47][48]. The SBS copolymer consists of three-dimensional styrene-butadiene-styrene chains, in which the rigid styrene domains are dispersed in a flexible butadiene matrix that serves as a continuous phase. When SBS is added to bitumen, the styrene blocks, through physical connections, can form three-dimensional networks that enable elastomers to give binders higher stiffness. When crumb rubber is added to the binder, it causes physical swelling and chemical degradation (devulcanization and depolymerization). Maltenes (light fractions of bitumen) are absorbed by rubber networks. This process is the main phenomenon that causes the swelling of crumb rubber (three-five times its original volume). In addition, a "gel" structure is formed at the bitumen/rubber interface. At this stage, effective stiffening of the binder takes place, which consequently affects the value of stiffness modulus of asphalt mixtures.
Due to the fact that asphalt mixtures are materials with visco-elastic properties, their technical features should be presented as a function of temperature change. The stiffness modulus of asphalt mixtures significantly decreases with increasing test temperature. This phenomenon results in a reduction in load-bearing capacity and load-carrying capability. Inverse changes are observed when the test temperature is decreased: the value of stiffness modulus begins to increase rapidly. This indicates that there is an increase in thermal stresses in the visco-elastic material. When the thermal stress value exceeds the tensile strength of the material, the initiation of low-temperature cracking occurs. When analyzing the results presented in Tables 6 and 7, it should be clearly stated that the stiffness modulus depends on many factors: type of mixture, type of binder used, amount of RG, test temperature, and frequency.
Considering the type of mixture, the highest values of the stiffness modulus were obtained at 5 • C at the frequency of 20 Hz for the mixture SMA8 with SBSM-2 + CRM-10 and CRM-10 binder (15,423 MPa and 14,978 MPa, respectively). On the other hand, the lowest values of modulus under the same test conditions were obtained for the mixture SMA8 LA (30% RG) with bitumen CRM-10 and SBSM-2 + CRM-10 (951 MPa and 964 MPa, respectively). It is a tenfold decrease in the value of the modulus in relation to the SMA8 LA mixture without the addition of RG (CRM-10-9680 MPa, SBSM-2 + CRM-10-10,057 MPa). It is worth emphasizing that the addition of another 10% of RG to the SMA8 LA mixture causes a decrease in the modulus value by approximately 50% in practically the entire range of analyzed temperatures. The lowest (favorable) temperature sensitivity (e.g., at the frequency of 10 Hz) in the group of mixtures without the addition of RG achieved the mixtures with SBSM-5 and SBSM-2 + CRM-10 binder (Figure 3). On the other hand, the highest (unfavorable) temperature sensitivity was shown by the mixtures with the reference bitumen 50/70. In mixtures where part of the aggregate was replaced with RG, the lowest sensitivity to temperature changes was found in the mixtures SMA8 LA (10% RG) with bitumen SBSM-5, SMA8 LA (20% RG) with SBSM-2 + CRM-10 binder, and SMA8 LA (30% RG) with CRM-10 binder. However, the most sensitive to temperature are the mixtures of SMA8 LA (10% RG and 20% RG) with bitumen 50/70 and SMA8 LA (30% RG) with the SBSM-5 binder.
Testing the stiffness modulus at variable frequencies of load application in the range from 0.5 Hz to 20 Hz allows for predicting the behavior of asphalt mixtures at variable vehicle speeds. The conducted tests proved that the temperature and the amount of RG have a significant influence on the change of the range of modulus values obtained at different load frequencies. The lowest discrepancies were obtained at 5 • C for mixtures without RG, the highest-at 25 • C for mixtures with 30% RG. This proves that at 5 • C the phase angle is much lower (higher stiffness of asphalt mixtures) than at 25 • C (Table 7). Low values of the stiffness modulus of mixtures with the addition of rubber granulate allow us to conclude that they will be able to transfer and withstand higher tensile stresses, thus allowing us to decrease the low-temperature cracking.
The second degree polynomial was used to describe the changes in the stiffness modulus values: where: Z-analyzed mixture parameter (stiffness modulus 4PB-PR); a 0 − a 14 -regression coefficients; X 1 -type of mixture; X 2 -type of binder; X 3 -temperature ( • C); X 4 -frequency (Hz).
The statistical analysis of the obtained results was started with the significance test using the ANOVA analysis of variance (STATISTICA software). The results of this analysis are presented in Table 8.  Where: Q-quadratic; L-linear.
Based on the analysis of the parameters, it can be clearly stated that the temperature, type of mixture and binder, and frequency are important factors affecting the stiffness modulus, because the p-value is lower than the assumed significance level α = 0.05 (p-Value < 0.05). Analyzing the square term referring to the type of binder (Type of Binder (Q)) and the factor describing the interaction of the binder type and frequency (2L·4L), no significant influence was found on the values of the stiffness modulus determinations. The values describing the parameters of the regression model are summarized in Table 9. On the basis of the analysis, it was observed that the value of the corrected determination coefficient was R 2 adj = 76%, which proves the correct adoption of the model.
The developed model of changes in the stiffness modulus can be presented using the following Relationship (10): The obtained regression model (Equation (10)) allows us to predict with good precision (about 76%) the stiffness modulus of the analyzed mixtures with SBS and crumb rubber modified binder (Figure 3).
The graphical interpretation of the 4PB-PR stiffness modulus change as a function of the type of mixture and binder is shown in Figure 4a, as a function of the binder type and temperature 4(b), and as a function of the binder type and frequency 4(c).

Phase Angle Φ
The changes in the phase angle Φ for the individual mixtures at different temperatures and frequencies are presented in Tables 10 and 11. A graphical interpretation of the change in phase angle, as a function of frequency at temperature 15 • C is shown in Figure 5.  5  23  20  17  16  14  15  35  33  27  25  24  25  44  42  39  38  37   SBSM-5   5  17  15  13  12  11  15  28  25  21  20  19  25  38  35  32  30  29   CRM-10   5  19  16  13  13  11  15  31  28  23  21  20  25  40  40  34  32  31   SBSM-2 + CRM-10   5  16  14  12  11  10  15  26  23  20  18  17  25  35  34 30 28 27 In the literature, there are few studies of the stiffness modulus tested using the 4PB-PR method. In addition, the authors of these publications hardly analyze the very important parameter, which is the phase angle, Φ. According to [49,50], the phase angle, Φ, mainly defines the viscoelastic properties of asphalt mixtures. It reflects the proportion of viscous and elastic parts in the asphalt mixtures. A lower value of the phase angle, Φ, indicates that elastic properties predominate in the mixture. In the case of mixtures with the base bitumen, the phase angle in the low-frequency area remained almost constant, and then gradually decreased with increasing frequency. A similar relationship was also observed in asphalt mixtures with modified binders, but the values of the phase angle, Φ, are lower in relation to mixtures with base bitumen, which is confirmed by the test results ( Figure 5). This proves that asphalt mixtures with modified binders are more rigid (the elastic phase dominates), while the mixtures with a conventional binder are more flexible (lower content of the elastic phase).  5  22  21  20  19  17  15  34  32  29  28  27  25  47  44  42  41  38   SBSM-5   5  20  19  16  15  15  15  31  28  26  23  20  25  42  37  34  33  31   CRM-10   5  24  21  18  16  13  15  34  29  28  27  25  25  41  39  38  37  35   SBSM-2 + CRM-10   5  23  19  18  16  12  15  30  28  25  24  21  25  42  37  36  35  32   SMA8 LA  (30% RG)   50/70   5  29  28  26  24  23  15  41  37  35  32  30  25  52  45  39  37  35   SBSM-5   5  25  21  20  16  15  15  35  33  29  28  24  25  42  42  38  36  32   CRM-10   5  25  23  21  19  19  15  33  32  29  28  22  25  45  42  39  35  35   SBSM-2 + CRM-10   5  25  25  22  20  20  15  34  32  30  28  24  25  43  42  38  36  35 When analyzing the obtained results of the phase angle, Φ, on the basis of the stiffness modulus tests using the 4PB-PR method presented in Tables 10 and 11 and in Figure 5; it should be stated that the type of binder, temperature, and frequency show a significant influence on the change of the phase angle, Φ. Mixtures with modified binders show higher values of the elastic component of the stiffness modulus (lower phase angle, Φ) in the entire range of tested temperatures and frequencies of loading. This fact proves that these mixtures are more resistant to accumulation and deformation in pavements compared to mixtures with conventional binders. For example, when analyzing the values of the phase angle, Φ, in the mixtures without the addition of RG at a temperature of 15 • C ( Figure 5), it is clearly visible that the best elastic properties were obtained by all the mixtures with modified binder SBSM-2 + CRM-10 (the smallest value of the phase angle, Φ). No such obvious difference can be observed in mixtures with the addition of RG. This proves that in these mixtures, the value of the phase angle, Φ, is mainly determined by the "elasticity" of RG. The type of mixture does not significantly affect the value of the phase angle, Φ, in the low frequency range of 0.5 Hz, 1 Hz, 5 Hz and temperatures of 5 • C and 15 • C ( Table 9). The greatest changes were observed only for the SMA8 LA (30% RG). On the other hand, the type of modified binder and the amount of RG additives have a significant impact.
Changes in this parameter at higher frequency ranges (10 Hz and 20 Hz) and test temperatures (25 • C) are significantly influenced by the type of binder, the amount of RG addition and the type of mixture.
The comprehensive description of the dependence of the phase angle, Φ, of asphalt mixtures with modified binder was made using the second degree polynomial: where: Z-analyzed mixture parameter (phase angle, Φ); a 0 − a 14 -regression coefficients; X 1 -type of mixture; X 2 -type of binder; X 3 -temperature ( • C); X 4 -frequency (Hz).
The first stage of model evaluation was to perform the significance test using ANOVA. The results of this analysis are presented in Table 12. The comprehensive statistical analysis of the parameters listed in Table 12 allows us to unequivocally state that the type of mixture and binder, temperature, and frequency are important factors affecting the phase angle, Φ, because the p-value related to them is lower than the assumed significance level α = 0.05. This relationship is not only observed with the square expression describing the influence of temperature. The existence of interactions between the type of mixture and the temperature, which affects the analyzed parameter (p-value less than α = 0.05), is of significant importance. The developed regression model of the dependence of the phase angle, Φ, in terms of the type of mixture and binder, temperature, and frequency are summarized in Table 13. Based on the analysis, it can be concluded that the value of the corrected determination coefficient equals R 2 adj = 92%, which proves the correct adoption of the model.
The developed model of the analyzed change in the phase angle, Φ, can be presented using the Equation (12) The obtained regression model (Equation (12)) allows to predict with very good precision (about 92%) the stiffness modulus of the analyzed mixtures with SBS and crumb rubber modified binder ( Figure 5).
The graphic interpretation of the change of the phase angle as a function of the type of mixture and binder is shown in Figure 6a, as a function of the type of binder and temperature in Figure 6b, and as a function of the type of binder and frequency in Figure 6c.

Conclusions
Based on the analysis of technical parameters obtained in the four-point bending test with prismatic samples of stone mastic mixtures SMA8, stone mastic asphalt reducing tire/road noise SMA8 LA and porous asphalt PA8 with SBS copolymer-modified binders, crumb rubber modified binders, and binders simultaneously modified with SBS and crumb rubber, the following conclusions were made: 1.
The type of modifier has a significant impact on the stiffness modulus of all analyzed asphalt mixtures, increasing its values in the entire range of analyzed temperatures from 5 • C to 25 • C. The highest values of the stiffness modulus were obtained at 5 • C and at the frequency of 20 Hz for the mixture of SMA8 with the binder SBSM-2 + CRM-10 and CRM-10 (15,423 MPa and 14,978 MPa). On the other hand, the lowest values of modulus under the same test conditions were obtained by the mixture SMA8 LA (30% RG), with bitumen CRM-10 and SBSM-2 + CRM-10 (951 MPa and 964 MPa, respectively).

3.
Replacing the mineral aggregate by another 10% rubber granulate in the SMA8 LA mixture causes a decrease in the stiffness modulus by about 50% in the entire range of analyzed temperatures.
The type of binder, the temperature, and the frequency show a significant influence on the change of the phase angle, Φ.

6.
Mixtures with the use of modified binders show higher values of the elastic component of the stiffness modulus (lower phase angle, Φ) in the entire range of tested temperatures and frequency of loading. This fact proves the greater resistance of these mixtures to accumulation and deformation in a pavement compared to mixtures with conventional binders. 7.
According to the analysis of the obtained test results, the optimal solution from a practical point of view is to use a binder simultaneously modified with 2% of SBS and 10% of crumb rubber for the production of low-noise asphalt mixtures. Mixtures SMA8 LA with the addition of 10% of rubber granulate are a good solution for applications in a climate where the average annual temperature is between 5-10 • C.

Funding:
The research was carried out as part of the research work No. WZ/WB-IIL/1/2020 at the Bialystok University of Technology and financed from a subsidy provided by the Polish Ministry of Science and Higher Education.
Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Data available in a publicly accessible repository.